Chapter 8.5, Problem 41PPS

To determine

To factor: The polynomial $9m{k}^2-15k^2+10-6m$

Answer to Problem 41PPS

  $\left(3m-5\right)\left(3k^2-2\right)$

Explanation of Solution

Given:

  $9m{k}^2-15k^2+10-6m$

Calculation:

The given polynomial is $9m{k}^2-15k^2+10-6m$

Make groups as shown below

  $\left(9m{k}^2-15k^2\right)+\left(10-6m\right)$

So, factored out the GCF from each of the group and then factored out the common factor

  $\begin{array}{l}\left(9m{k}^2-15k^2\right)+\left(10-6m\right)\\ =3k^2\left(3m-5\right)-2\left(3m-5\right)\\ =\left(3m-5\right)\left(3k^2-2\right)\end{array}$

So, the factored form is $\left(3m-5\right)\left(3k^2-2\right)$